A well-known fact about household savings behaviour is that it depends on an
individual's own wealth holdings and income expectations. In understanding
how these decisions aggregate and respond to policy, we must therefore
confront the substantial heterogeneity in these features which is present in
the macro economy. One persistent challenge in the literature which aims
to provide this understanding is the need to keep track of and forecast the
decisions of every single individual in the economy. Such a feat is not possible
in practice, so that some grouping of individuals is typically needed to sidestep
the issue.

This article considers the dividing of households into representative groups
to optimally represent savings decisions across the wealth distribution. Such
a division is guided by the principle that many groups are needed where
there is a large amount of variation in savings propensities. Combining
numerical analysis with theory on consumption behaviour, it is shown in
the context of a simple model that the savings behaviour of wealthy and
poor households can be captured by including a single representative for each
category. Meanwhile, several groups are needed to describe the behaviour
of the middle class. Middle class households face uncertain future income
comparable in size to current wealth holdings, leading to a wide range of
savings propensities when compared to poor hand-to-mouth individuals and
wealthy savers.